The difference is in the design of the head. Also due to the head design, the physical size of the motor is larger even if CID (displacement) is identical.
The best visual example I can think of is Ford 351 windsor which was a small block and a Ford 351 cleveland which was a big block:
Generally you can tell the difference by looking at the valve covers. if they are long, narrow and rectangular, it's a small block. If they are fat squat and irregular shaped, you're looking at a big block.
There are other differences too, for example bore and stroke. A small block generally has a shorter stroke and is thought to rev higher, whereas a big block has a longer stroke with more torque.
There are other disputed difference between a small and a big block. And for the most part, you can simply tell by the displacement. Generally, anything larger than 366 CID is a big block.